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/*
Copyright (C) 2020 Fredrik Johansson
This file is part of FLINT.
FLINT is free software: you can redistribute it and/or modify it under
the terms of the GNU Lesser General Public License (LGPL) as published
by the Free Software Foundation; either version 3 of the License, or
(at your option) any later version. See <https://www.gnu.org/licenses/>.
*/
#include "ca.h"
truth_t
ca_check_equal(const ca_t x, const ca_t y, ca_ctx_t ctx)
{
acb_t u, v;
ca_t t;
truth_t res;
truth_t x_alg, y_alg;
slong prec;
if (CA_IS_QQ(x, ctx) && CA_IS_QQ(y, ctx))
{
return fmpq_equal(CA_FMPQ(x), CA_FMPQ(y)) ? T_TRUE : T_FALSE;
}
if (CA_IS_SPECIAL(x) || CA_IS_SPECIAL(y))
{
if (CA_IS_UNKNOWN(x) || CA_IS_UNKNOWN(y))
return T_UNKNOWN;
if (CA_IS_SIGNED_INF(x) && CA_IS_SIGNED_INF(y))
{
ca_t xsign, ysign;
*xsign = *x;
*ysign = *y;
xsign->field &= ~CA_SPECIAL;
ysign->field &= ~CA_SPECIAL;
return ca_check_equal(xsign, ysign, ctx);
}
if (x->field == y->field)
return T_TRUE;
else
return T_FALSE;
}
if (ca_equal_repr(x, y, ctx))
return T_TRUE;
/* same algebraic number field ==> sufficient to compare representation */
if (x->field == y->field && CA_FIELD_IS_NF(CA_FIELD(x, ctx)))
return T_FALSE;
/* Rational number field elements *should* have been demoted to QQ
automatically, but let's do a comparison as a precaution. */
if (CA_FIELD_IS_NF(CA_FIELD(x, ctx)) && CA_IS_QQ(y, ctx))
return nf_elem_equal_fmpq(CA_NF_ELEM(x), CA_FMPQ(y), CA_FIELD_NF(CA_FIELD(x, ctx))) ? T_TRUE : T_FALSE;
if (CA_FIELD_IS_NF(CA_FIELD(y, ctx)) && CA_IS_QQ(x, ctx))
return nf_elem_equal_fmpq(CA_NF_ELEM(y), CA_FMPQ(x), CA_FIELD_NF(CA_FIELD(y, ctx))) ? T_TRUE : T_FALSE;
res = T_UNKNOWN;
acb_init(u);
acb_init(v);
/* for (prec = 64; (prec <= ctx->options[CA_OPT_PREC_LIMIT]) && (res == T_UNKNOWN); prec *= 2) */
prec = 64;
{
ca_get_acb_raw(u, x, prec, ctx);
ca_get_acb_raw(v, y, prec, ctx);
if (!acb_overlaps(u, v))
{
res = T_FALSE;
}
}
acb_clear(u);
acb_clear(v);
x_alg = ca_check_is_algebraic(x, ctx);
y_alg = ca_check_is_algebraic(y, ctx);
if ((x_alg == T_TRUE && y_alg == T_FALSE) ||
(x_alg == T_FALSE && y_alg == T_TRUE))
return T_FALSE;
/* todo: try qqbar computation */
/* we may want to do this selectively; in some cases cancellation in
computing x-y will be helpful; in other cases, subtracting the
terms will make life more difficult */
if (0 && x_alg == T_TRUE && y_alg == T_TRUE)
{
/* ...
qqbar_t a, b;
qqbar_init(a);
qqbar_init(b);
if (ca_get_qqbar(a, x, ctx))
{
if (ca_get_qqbar(b, y, ctx))
{
int eq = qqbar_equal(a, b);
qqbar_clear(a);
qqbar_clear(b);
return eq ? T_TRUE : T_FALSE;
}
}
qqbar_clear(a);
qqbar_clear(b);
*/
}
if (res == T_UNKNOWN)
{
/* check_is_zero may have additional heuristics */
ca_init(t, ctx);
ca_sub(t, x, y, ctx);
res = ca_check_is_zero(t, ctx);
ca_clear(t, ctx);
}
return res;
}